A sampling approach to bandlimiting instantaneously companded signals

A well-known theorem of Beurling demonstrates that distinct bandlimited signals remain distinct after instantaneous companding and ideal low-pass filtering. Motivated by this result, Landau (1960) developed an iterative method for recovering a bandlimited signal after companding and low-pass filtering. This paper describes an alternative to low-pass filtering for restoring the original bandwidth to a companded bandlimited signal prior to transmission on a bandlimited channel. This approach allows the original signal to be recovered without iteration, but it also introduces some synchronization issues. These issues are examined and the design of companding functions that endow the transmitted signal with desired characteristics is considered.